Here's the deal:
When you fret a note, you are stretching the string. The shortest distance between two points is a straight line, so when you force the string to go from the bridge saddle, to a fret, to the nut, it has to get longer. Stretching a string, will, of course, make it higher-pitched. The frets are all placed 1/18 (more like 17.819etc., but who's counting?) of the distance from the previous fret to the bridge.
Still with me? Good. So you know that different gauge strings need to be bent different distances to reach the same pitch? Try it, a set of .009's is easy to bend, but you have to use up a ton of fretboard to reach a given pitch, compared to say, a set of .011's on the same guitar. Trust me, it's true.
So now, the fun part. Depending on where you fret, you are stretching the string a different distance. At the first fret, you are usually going the least distance, at the last fret, about the most (assuming your action gets progressively higher as you head towards the bridge, which is almost always true). As suggested in the previous paragraph, the degree to which you are stretching a string to fret it varies on a given fret, depending on the gauge/tension of the string. Therefore, the 1/18th rule for positioning frets [b[]cannot[/b] result in a correctly intonated guitar!
So, now on to your example. Your thong, er, G string, is getting flatter towards the bridge. An easy fix, detune the string until it's floppy, loosen the screw on the back of the trem so that the saddle moves towards the nut (shorter means sharper), retune, and check the higher frets. Repeat until the 12th and higher frets are behaving themselves pretty well, and again for the other strings.
Now would be a good time to check for relief, just on principal. Fret the first and last fret, and peak at the space between the string and seventh fret. You'd like to see just a bit of light, somewhere around .009 to .011. You probably have strings that size, use one as a gauge. If you have too much relief, tighten the truss rod maybe 1/8th a turn, and let it sit overnight. It will take a while for the adjustment to settle in, and if you strip or break the rod, you're all done. The truss rod should turn smoothly, but with some tension. It will help to loosen the strings, or bend the neck forward as you tighten. If the nut seems stuck, you're probably out of adjustment, and it will need a luthier to fiddle with it.
On most guitars, the nut slots are not cut deep enough, which prevents open string buzzing, but also causes sharp notes near the nut. Ideally, you would cut the slots deeper, so that the first frets are pretty much in tune, the depth of the nut slots will affect the first five or so frets far more than saddle adjustment, and trying to get these frets intonated from the saddles will screw up the intonation starting at the 12th fret or so.
I know, nobody has the unique files required to cut nut slots. Neither do I.
Option one, intonate for the first few frets, and live with it. If your initials are Malcom Young, this will be fine. Option two, adjust the intonation so the 12th fret harmonic is the exact same note as the 12th fretted fret. You'll be a bit out at both ends, but not felonously so. If you have another guitar player, you may be noticably off-pitch when the two of you are at opposite ends of the board. Option three, cough up the money for a pro set-up. He should get the nut right the first time, and you will be fine forever, as long as you don't change string gauges. Option four, cough up the loot for fret files, and go slowly. If you cut too deep, and go sharp or get buzzing, fill in the slot with a little super glue or epoxy, and start over.
Also keep in mind, that you are never going to completely intonate the guitar, it's impossible. You will be a bit out here and there, but hopefully, you won't be wildly out at adjacent notes, so you can play barre chords wherever you want. Guitar oriented music has evolved around the parts of the fretboard, and types of chords that are reasonably intonated, and avoiding the trouble spots. The Buzz Feiten system uses a compesated nut, and specially mistuned open strings to create a very nearly in-tune instrument, but it hasn't been used by enough people long enough to unleash the entire freboard.
Simple, right?
